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Dynamic Time Warping (DTW) is widely used as a similarity measure in various domains. Due to its invariance against warping in the time axis, DTW provides more meaningful discrepancy measurements between two signals than other distance measures. In this paper, we propose a novel component in an artificial neural network. In contrast to the previous successful usage of DTW as a loss function, the proposed framework leverages DTW to obtain a better feature extraction. For the first time, the DTW loss is theoretically analyzed, and a stochastic backpropogation scheme is proposed to improve the accuracy and efficiency of the DTW learning. We also demonstrate that the proposed framework can be used as a data analysis tool to perform data decomposition. 

Recommendation for e-commerce with a mix of durable and nondurable goods has characteristics that distinguish it from the well-studied media recommendation problem. The demand for items is a combined effect of form utility and time utility, i.e., a product must both be intrinsically appealing to a consumer and the time must be right for purchase. In particular for durable goods, time utility is a function of inter-purchase duration within product category because consumers are unlikely to purchase two items in the same category in close temporal succession. Moreover, purchase data, in contrast to rating data, is implicit with non-purchases not necessarily indicating dislike. Together, these issues give rise to the positive-unlabeled demand-aware recommendation problem that we pose via joint low-rank tensor completion and product category inter-purchase duration vector estimation. We further relax this problem and propose a highly scalable alternating minimization approach with which we can solve problems with millions of users and millions of items in a single thread. We also show superior prediction accuracies on multiple real-world datasets.